Early statistics in kindergarten: analysis of an educator's pedagogical content knowledge in lessons promoting informal inferential reasoning

PurposeThis study aims to describe the pedagogical content knowledge (PCK) of a kindergarten educator who implements a lesson plan about informal inferential reasoning designed in a lesson study group.Design/methodology/approachTo this end, we analyzed teaching interventions in two kindergarten lessons focused on the playful task of tossing two coins, associated with inferential statistical reasoning. The study highlights the importance of arguing and promoting this reasoning to develop statistical thinking. It is crucial to recognize how early students can be subject to learning experiences that promote a language of uncertainty, assess the evidence provided by the data, and make generalizations.FindingsThe results reveal that while the educator demonstrated knowledge and skills relevant to the curriculum and conceptual teaching strategies, the understanding of the content by the students and the integration of the PCK components still present a challenge.Practical implicationsThe lesson study collaborative teaching practices that promote PCK have proven effective for informing the design and implementation of instructional practices supporting the development of early statistical thinking in young children.Originality/valueThe study enriches the knowledge regarding the potential of the lesson study (LS) in the professional learning of kindergarten educators. It also contributes to a comprehensive approach based on authentic playful experiences in grade K that supports the development of early statistical thinking in young children.

Desarrollo de la Investigación en Razonamiento Inferencial Informal

En este trabajo se informa sobre una Revisión Sistemática de la Literatura (SLR) basada en la búsqueda automatizada en WoS, Scopus, MathEduc y, adicionalmente, en el SERJ de forma manual. El objetivo es proporcionar un panorama general del desarrollo de la investigación en el Razonamiento Inferencial Informal (RII) para investigadores en Educación Estadística. De los resultados de la búsqueda, se seleccionaron 57 estudios primarios, identificando el énfasis, el contexto y la metodología de las investigaciones; así como los autores y artículos más citados. Se encontró que en los últimos años, el desarrollo de la investigación en RII se ha enfocado en la modelación y el uso de software dinámico; los resultados están dirigidos a investigadores y profesores. Cabe destacar que los artículos con mayor impacto, en cuestión del número de citas o promedio de citas por año, son aquellos estudios previos que se consideran íconos dentro de la Educación Estadística, ya que proponen un marco de trabajo enfocado en la integración de conceptos o ideas estadísticas como un sistema para el desarrollo del RII. Abstract This paper reports on a Systematic Literature Review (SLR) based on the automated search in WoS, Scopus, MathEduc and, additionally, manually in SERJ. The aim is to provide an overview of the development of research in Informal Inferential Reasoning (IIR) for researchers in Statistical Education. From the search results, 57 primary studies were selected, identifying the emphasis, context and methodology; as well as the most cited authors and articles. It was found that in recent years, the development of research in the IIR has focused on the modeling and use of dynamic software; the results are aimed at researchers and professors. It should be noted that the articles with the greatest impact, in terms of the number of citations or average citations per year, are those previous studies that are considered essential within Statistical Education, since they propose a framework focused on integration of concepts or statistical ideas as a system for the development of the RII

ASSESSMENT OF INFORMAL AND FORMAL INFERENTIAL REASONING: A CRITICAL RESEARCH REVIEW

As a contribution to the discussion on the assessment of informal inferential reasoning (IIR) and the transition from this to formal inferential reasoning (FIR), we present a review of research on how these two types of inferential reasoning have been conceptualized and assessed. Based on our review, we discuss the need to redefine the conceptions of IIR and FIR in order to create an integrated description of inferential reasoning that includes not only ideas of IIR and FIR, but also the whole activity of argumentation, which involves the production of both statistical and contextual reasons. Current descriptions of IIR and FIR list the facts that might be brought from data analysis to the process of inferential reasoning. The approach we propose considers how the facts, both statistical and contextual, can be used as arguments, leading to assessments of students’ inferential reasoning focusing on articulating the statistical and contextual reasons students present to support an inference. First published May 2019 at Statistics Education Research Journal Archives

PEMBELAJARAN UNTUK MENGEMBANGKAN KEMAMPUAN PENALARAN INFERENSIAL STATISTIS

Abstrak: Artikel ini membahas tentang pembelajaran yang dapat digunakan untuk mengembangkan kemampuan penalaran inferensial statistis. Tujuan kognitif pembelajaran Statistika adalah untuk mengembangkan kemampuan literasi, penalaran, dan berpikir statistis. Salah satu tujuan dalam penalaran statistis adalah mengembangkan kemampuan penalaran inferensial. Model pembelajaran yang dapat digunakan untuk mengembangkan kemampuan penalaran inferensial statistis adalah model Statistical Reasoning Learning Environment (SRLE) yang didasarkan pada teori belajar konstruktivisme. Analisis didasarkan pada: 1) definisi inferensi statistis; 2) definisi penalaran inferensial informal dan formal; 3) kerangka kerja penalaran inferensial informal; 5) model pembelajaran SRLE; dan 6) penelitian terkait penalaran inferensial statistis.Abstract: This article deals with learning that can be used to develop inferential reasoning abilities statistically. The cognitive goal of statistical learning is to develop literacy, reasoning, and statistical thinking skills. One of the goals in statistical reasoning is to develop inferential reasoning abilities. The learning model that can be used to develop static inferential reasoning abilities is Statistical Reasoning Learning Environment (SRLE) model based on constructivism learning theory. The analysis is based on: 1) the definition of statistical inference; 2) the definition of informal and formal inferential reasoning; 3) informal inferential reasoning framework; 5) the learning model of SRLE; and 6) research related to inferential statistical reasoning.

A MODELING APPROACH TO THE DEVELOPMENT OF STUDENTS’ INFORMAL INFERENTIAL REASONING

Teaching from an informal statistical inference perspective can address the challenge of teaching statistics in a coherent way. We argue that activities that promote model-based reasoning address two additional challenges: providing a coherent sequence of topics and promoting the application of knowledge to novel situations. We take a models and modeling perspective as a framework for designing and implementing an instructional sequence of model development tasks focused on developing primary students’ generalized models for drawing informal inferences when comparing two sets of data. This study was conducted with 26 Year 5 students (ages 10-11). Our study provides empirical evidence for how a modeling perspective can bring together lines of research that hold potential for the teaching and learning of inferential reasoning. First published November 2017 at Statistics Education Research Journal Archives

THE EMERGENCE OF PROBABILISTIC LANGUAGE FROM STUDENTS’ UNCERTAINTY IN LEARNING INFORMAL INFERENTIAL REASONING

In our daily life, we often draw conclusion regarding some phenomenon to get new information from sampleof the population. By doing so, we unconsciously learn the inferential statistics informally or known as Informal Inferential Reasoning (IIR). Therefore, it can be said that IIR is close to our live. As a result, it is wise to use IIR in introducing inferential statistics to students. In introducing IIR, a set of learning design needs to be made. In this research, the design would use Realistic Mathematics Education (RME) as the approach of the learning and dot plot as a visual representation. This paper describes the probabilistic language students used in expressing some uncertainty when making generalization. The method used is design research. The involved subjects in this research were six students of VII-8 at SMPN 7 Tangerang Selatan. The results showed that the probabilistic language appears when students generalize the data. Moreover, probabilistic language also appears when students added samples in growing sample activity. Probablistic language which appeared in this research are “mungkin”, “hampir sama”, “kurang sama”, and so on. Keywords : design research; informal inferential reasoning; probabilistic language; uncertainty.